Details

Time bar (total: 47.0s)

sample116.0ms

Algorithm
intervals
Results
27.0ms294×body80nan
24.0ms130×body160valid
24.0ms550×pre80true
19.0ms126×body80valid

simplify162.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
162.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.2b

localize34.0ms

Local error

Found 4 expressions with local error:

27.0b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.2b
(fma c (* -4 a) (* b b))
0.1b
(sqrt (fma c (* -4 a) (* b b)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef flip-- associate-/l/
Counts
4 → 179
Calls
4 calls:
Slowest
24.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
8.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series413.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
112.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
104.0ms
(sqrt (fma c (* -4 a) (* b b)))
77.0ms
(fma c (* -4 a) (* b b))

simplify16.2s

Counts
225 → 191
Calls
225 calls:
Slowest
489.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) (sqrt 2)) a)
476.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
287.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
239.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
191.0ms
(/ (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (* (* a a) a))

prune2.4s

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 24.5b

localize28.0ms

Local error

Found 4 expressions with local error:

27.0b
(- (sqrt (fma b b (* (* a -4) c))) b)
0.3b
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
0.1b
(sqrt (fma b b (* (* a -4) c)))
0.0b
(fma b b (* (* a -4) c))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
31×*-un-lft-identity
27×add-cube-cbrt
18×prod-diff
17×sqrt-prod
13×associate-*r*
10×times-frac
9×add-cbrt-cube add-exp-log
7×pow1
6×fma-neg associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×flip3-- flip--
2×frac-times associate-*l/ prod-exp cbrt-unprod distribute-lft-out-- unswap-sqr
1×cbrt-undiv rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log div-exp pow-prod-down associate-*r/ *-commutative fma-udef div-inv
Counts
4 → 111
Calls
4 calls:
Slowest
40.0ms
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
8.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
2.0ms
(sqrt (fma b b (* (* a -4) c)))
0.0ms
(fma b b (* (* a -4) c))

series501.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
134.0ms
(sqrt (fma b b (* (* a -4) c)))
132.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
62.0ms
(fma b b (* (* a -4) c))

simplify6.2s

Counts
96 → 123
Calls
96 calls:
Slowest
535.0ms
(* (- (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (* b b)) 1/2)
358.0ms
(* (+ (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (+ (* b b) (* (sqrt (fma b b (* (* a -4) c))) b))) a)
283.0ms
(* (- (pow (sqrt (fma b b (* (* a -4) c))) 3) (pow b 3)) (/ 1/2 a))
271.0ms
(- b (* 2 (/ (* a c) b)))
239.0ms
(* (- (pow (sqrt (fma b b (* (* a -4) c))) 3) (pow b 3)) 1/2)

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1/2 a) (fma a (* c -4) 0))
0.2b
(+ (sqrt (fma b b (* (* a -4) c))) b)
0.2b
(/ (* (/ 1/2 a) (fma a (* c -4) 0)) (+ (sqrt (fma b b (* (* a -4) c))) b))
0.1b
(sqrt (fma b b (* (* a -4) c)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt *-un-lft-identity
18×add-cbrt-cube add-exp-log
17×add-cube-cbrt
14×times-frac
13×associate-*l*
7×pow1
6×fma-def sqrt-prod add-log-exp
5×cbrt-undiv div-exp
4×expm1-log1p-u associate-/r* prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×associate-*r* distribute-lft-out
2×flip3-+ associate-*l/ associate-/r/ flip-+ fma-udef div-inv unswap-sqr
1×distribute-rgt-in +-commutative rem-sqrt-square clear-num sum-log frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down *-commutative associate-/l* associate-/l/
Counts
4 → 105
Calls
4 calls:
Slowest
32.0ms
(/ (* (/ 1/2 a) (fma a (* c -4) 0)) (+ (sqrt (fma b b (* (* a -4) c))) b))
19.0ms
(* (/ 1/2 a) (fma a (* c -4) 0))
12.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
1.0ms
(sqrt (fma b b (* (* a -4) c)))

series598.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
292.0ms
(/ (* (/ 1/2 a) (fma a (* c -4) 0)) (+ (sqrt (fma b b (* (* a -4) c))) b))
132.0ms
(sqrt (fma b b (* (* a -4) c)))
116.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
59.0ms
(* (/ 1/2 a) (fma a (* c -4) 0))

simplify7.4s

Counts
72 → 117
Calls
72 calls:
Slowest
1.1s
(* (* (* (/ 1/2 a) (/ 1/2 a)) (/ 1/2 a)) (* (* (fma a (* c -4) 0) (fma a (* c -4) 0)) (fma a (* c -4) 0)))
513.0ms
(/ (* (/ (* (* 1/2 1/2) 1/2) (* (* a a) a)) (* (* (fma a (* c -4) 0) (fma a (* c -4) 0)) (fma a (* c -4) 0))) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
481.0ms
(/ (* (* (* (/ 1/2 a) (fma a (* c -4) 0)) (* (/ 1/2 a) (fma a (* c -4) 0))) (* (/ 1/2 a) (fma a (* c -4) 0))) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
457.0ms
(+ (- (log 1/2) (log a)) (log (fma a (* c -4) 0)))
417.0ms
(/ (* (* (* (/ 1/2 a) (/ 1/2 a)) (/ 1/2 a)) (* (* (fma a (* c -4) 0) (fma a (* c -4) 0)) (fma a (* c -4) 0))) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (sqrt (fma b b (* (* a -4) c))) b)
0.2b
(/ (* -2 c) (+ (sqrt (fma b b (* (* a -4) c))) b))
0.1b
(sqrt (fma b b (* (* a -4) c)))
0.0b
(fma b b (* (* a -4) c))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
10×add-sqr-sqrt
9×add-cbrt-cube add-exp-log add-cube-cbrt
6×fma-def sqrt-prod add-log-exp
5×pow1
4×expm1-log1p-u associate-/r* times-frac insert-posit16 log1p-expm1-u
3×distribute-lft-out
2×cbrt-undiv flip3-+ div-exp associate-/r/ flip-+
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod fma-udef div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
Slowest
20.0ms
(/ (* -2 c) (+ (sqrt (fma b b (* (* a -4) c))) b))
6.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
2.0ms
(sqrt (fma b b (* (* a -4) c)))
0.0ms
(fma b b (* (* a -4) c))

series590.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
272.0ms
(/ (* -2 c) (+ (sqrt (fma b b (* (* a -4) c))) b))
135.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
105.0ms
(sqrt (fma b b (* (* a -4) c)))
77.0ms
(fma b b (* (* a -4) c))

simplify3.0s

Counts
42 → 88
Calls
42 calls:
Slowest
402.0ms
(+ (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (- (* b b) (* (sqrt (fma b b (* (* a -4) c))) b)))
275.0ms
(/ (* (* (* -2 c) (* -2 c)) (* -2 c)) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
250.0ms
(- b (* 2 (/ (* a c) b)))
246.0ms
(/ (* (* (* -2 -2) -2) (* (* c c) c)) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
233.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))

prune898.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes270.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.0s4510×body160valid
1.2s8323×body80nan
1.1s16323×pre80true
557.0ms3490×body80valid